The equation to graph is:

$5x + 5y = 15$

Steps to Graph the Equation:

1. Simplify the equation: Divide the entire equation by 5 to simplify: $x + y = 3$ Now, we have the equation in a simpler form.

2. Rewrite in slope-intercept form: $y = -x + 3$ This equation is in the form $y = mx + b$, where:

   • $m = -1$ is the slope (indicating a downward slope),
   • $b = 3$ is the y-intercept (the point where the line crosses the y-axis).

3. Plot the y-intercept:

   • Start by plotting the point (0, 3) on the y-axis.

4. Use the slope:

   • The slope is -1, which means for every 1 unit you move to the right along the x-axis, move 1 unit down.
   • From the point (0, 3), move right 1 unit and down 1 unit to get the point (1, 2). Plot this point.

5. Draw the line:

   • Draw a straight line through the points (0, 3) and (1, 2), extending in both directions.

Would you like me to generate a graph for this equation?

Follow-up Questions:

1. What is the importance of slope-intercept form in graphing linear equations?
2. How do you find the slope from a linear equation in standard form?
3. What does the y-intercept tell you about the graph of a linear equation?
4. Can you convert any linear equation into slope-intercept form?
5. How can you check if a point lies on the graph of a linear equation?

Tip:

When graphing a linear equation, always start by identifying the y-intercept and the slope, as they provide a clear starting point and direction for the line.